Let H(t) by the air temperature in degrees Fahrenheit in San Antonio t hours aft

Question

Let H(t) by the air temperature in degrees Fahrenheit in San Antonio t hours after 8 AM on a calm winter day. The large graph on the next page shows the derivative H'(t) - that is, of rate of change of the temperature - as. a function of f, the number of hours after 8 AM. (a) According to the graph. at what time does the temperature stop increasing? (b) Estimate the change in the temperature on the day shown from 8 AM to 8 PM. Show your work so that 1 can understand the approach you are taking. (c) Explain why it is impossible for us to determine the temperature at 8 PM based on the graph given. (d) Suppose we are given that the temperature at noon on the day shown was 54 degree F. What were the temperatures at 8 AM and at 8 PM?

Explanation / Answer

a> at t =9 , that is 9 hours from the start the air temperature is the maximum , its eviden from the graph.

we know that when the derivative is 0 then at that point we'll get the opyimum value. And after t=9 the graph of H'(t) becomes negative , this indicates that H(t) is decreasing after t = 9.

so after t=9 hours H(t) stopped increasing.

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